Circle corner (a two-dimensional figure) is a right triangle having acute vertices on a circle with the hypotenuse outside the circle.
- Chord is a line segment on the interior of a circle.
- Segment of a circle is an interior part of a circle bound by a chord and an arc.
area of a Circle Corner formula
\(\large{ A_{area} = \frac{a\;b \;-\; r \; l \;+\; s \; \left(r \;-\; h\right) }{2 } }\) |
|
Where:
Units |
English |
SI |
\(\large{ A_{area} }\) = area |
\(\large{ft^2}\) |
\(\large{m^2}\) |
\(\large{ l }\) = arc length |
\(\large{ft}\) |
\(\large{m}\) |
\(\large{ s }\) = chord length |
\(\large{ft}\) |
\(\large{m}\) |
\(\large{ a, b }\) = edge |
\(\large{ft}\) |
\(\large{m}\) |
\(\large{ r }\) = radius |
\(\large{ft}\) |
\(\large{m}\) |
\(\large{ h }\) = segment height |
\(\large{ft}\) |
\(\large{m}\) |
Arc Length of a Circle Corner formula
\(\large{ l = r \; \theta }\) |
|
Where:
Units |
English |
SI |
\(\large{ l }\) = arc length |
\(\large{ft}\) |
\(\large{m}\) |
\(\large{ \theta }\) = angle |
\(\large{deg}\) |
\(\large{rad}\) |
\(\large{ r }\) = radius |
\(\large{ft}\) |
\(\large{m}\) |
Chord Length of a Circle Corner formula
\(\large{ s = a^2 \; b^2 }\) |
|
Where:
Units |
English |
SI |
\(\large{ s }\) = chord length |
\(\large{ft}\) |
\(\large{m}\) |
\(\large{ a, b }\) = edge |
\(\large{ft}\) |
\(\large{m}\) |
Height of a Circle Corner formula
\(\large{ h = r \; \left( 1 - cos \; \frac{\theta}{2} \right) }\) |
|
Where:
Units |
English |
SI |
\(\large{ h }\) = segment height |
\(\large{ft}\) |
\(\large{m}\) |
\(\large{ \theta }\) = segment angle |
\(\large{deg}\) |
\(\large{rad}\) |
\(\large{ r }\) = radius |
\(\large{ft}\) |
\(\large{m}\) |
Perimeter of a Circle Corner formula
\(\large{ p = a + b + l }\) |
|
Where:
Units |
English |
SI |
\(\large{ p }\) = perimeter |
\(\large{ft}\) |
\(\large{m}\) |
\(\large{ l }\) = arc length |
\(\large{ft}\) |
\(\large{m}\) |
\(\large{ a, b }\) = edge |
\(\large{ft}\) |
\(\large{m}\) |
Segment Angle of a Circle Corner formula
\(\large{ \theta = arccos \; \frac{ 2\;r^2 \;-\; s^2 }{2\;r^2} }\) |
|
Where:
Units |
English |
SI |
\(\large{ \theta }\) = segment angle |
\(\large{deg}\) |
\(\large{rad}\) |
\(\large{ s }\) = chord length |
\(\large{ft}\) |
\(\large{m}\) |
\(\large{ r }\) = radius |
\(\large{ft}\) |
\(\large{m}\) |
Tags:
Equations for Area
Equations for Perimeter
Equations for Arc Length
Equations for Chord
Equations for Segment